Simplify the following expression: $ p = \dfrac{-8n + 9}{n + 7} - 9 $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the second expression by $\dfrac{n + 7}{n + 7}$ $ \dfrac{9}{1} \times \dfrac{n + 7}{n + 7} = \dfrac{9n + 63}{n + 7} $ Therefore $ p = \dfrac{-8n + 9}{n + 7} - \dfrac{9n + 63}{n + 7} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-8n + 9 - (9n + 63) }{n + 7} $ Distribute the negative sign: $p = \dfrac{-8n + 9 - 9n - 63}{n + 7}$ $p = \dfrac{-17n - 54}{n + 7}$